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Simplifying 15x2 + -50 + x = 500x Reorder the terms: -50 + x + 15x2 = 500x Solving -50 + x + 15x2 = 500x Solving for variable 'x'. Reorder the terms: -50 + x + -500x + 15x2 = 500x + -500x Combine like terms: x + -500x = -499x -50 + -499x + 15x2 = 500x + -500x Combine like terms: 500x + -500x = 0 -50 + -499x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -3.333333333 + -33.26666667x + x2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -33.26666667x + 3.333333333 + x2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -33.26666667x + x2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -33.26666667x + x2 = 0 + 3.333333333 -33.26666667x + x2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -33.26666667x + x2 = 3.333333333 The x term is -33.26666667x. Take half its coefficient (-16.63333334). Square it (276.6677780) and add it to both sides. Add '276.6677780' to each side of the equation. -33.26666667x + 276.6677780 + x2 = 3.333333333 + 276.6677780 Reorder the terms: 276.6677780 + -33.26666667x + x2 = 3.333333333 + 276.6677780 Combine like terms: 3.333333333 + 276.6677780 = 280.001111333 276.6677780 + -33.26666667x + x2 = 280.001111333 Factor a perfect square on the left side: (x + -16.63333334)(x + -16.63333334) = 280.001111333 Calculate the square root of the right side: 16.733233738 Break this problem into two subproblems by setting (x + -16.63333334) equal to 16.733233738 and -16.733233738.Subproblem 1
x + -16.63333334 = 16.733233738 Simplifying x + -16.63333334 = 16.733233738 Reorder the terms: -16.63333334 + x = 16.733233738 Solving -16.63333334 + x = 16.733233738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.63333334' to each side of the equation. -16.63333334 + 16.63333334 + x = 16.733233738 + 16.63333334 Combine like terms: -16.63333334 + 16.63333334 = 0.00000000 0.00000000 + x = 16.733233738 + 16.63333334 x = 16.733233738 + 16.63333334 Combine like terms: 16.733233738 + 16.63333334 = 33.366567078 x = 33.366567078 Simplifying x = 33.366567078Subproblem 2
x + -16.63333334 = -16.733233738 Simplifying x + -16.63333334 = -16.733233738 Reorder the terms: -16.63333334 + x = -16.733233738 Solving -16.63333334 + x = -16.733233738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.63333334' to each side of the equation. -16.63333334 + 16.63333334 + x = -16.733233738 + 16.63333334 Combine like terms: -16.63333334 + 16.63333334 = 0.00000000 0.00000000 + x = -16.733233738 + 16.63333334 x = -16.733233738 + 16.63333334 Combine like terms: -16.733233738 + 16.63333334 = -0.099900398 x = -0.099900398 Simplifying x = -0.099900398Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.366567078, -0.099900398}
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